Stable distribution and long-range correlation of Brent crude oil market

An empirical study of stable distribution and long-range correlation in Brent crude oil market was presented. First, it is found that the empirical distribution of Brent crude oil returns can be fitted well by a stable distribution, which is significantly different from a normal distribution. Second, the detrended fluctuation analysis for the Brent crude oil returns shows that there are long-range correlation in returns. It implies that there are patterns or trends in returns that persist over time. Third, the detrended fluctuation analysis for the Brent crude oil returns shows that after the financial crisis 2008, the Brent crude oil market becomes more persistence. It implies that the financial crisis 2008 could increase the frequency and strength of the interdependence and correlations between the financial time series. All of these findings may be used to improve the current fractal theories.